There is a reason no one has bothered with this. The issue of locality has been settled and understood for a long time, and it has especially been clear since the GHZ example was discovered that statistical issues such as whatever you plan to obfuscate with are completely irrelevant. Or, to make your supposed challenge apparently much harder to meet, let's actually take all considerations of probability theory at all out of the discussion. Here's your challenge: Show how to create a local state of three particles such that they will give quantum-mechanically acceptable results *on a single run* no matter which of the four possible relevant experimental configurations is chosen. On a single run. No statistics. No averages.No measuring more than one thing by any of the three experimenters.

You can't do it. The proof is so obvious that anyone can follow it. No averages, so no issues about averages. Put up or shut up.

By the bye, the logic of the conclusion of your paper is this: you think that because you derived an inequality by making a certain manifestly ridiculous assumption you have "proven" that other derivations make the same ridiculous assumption. There is an obvious reason no one finds it necessary to respond.

Tim Maudlin wrote:There is a reason no one has bothered with this. The issue of locality has been settled and understood for a long time, and it has especially been clear since the GHZ example was discovered that statistical issues such as whatever you plan to obfuscate with are completely irrelevant. Or, to make your supposed challenge apparently much harder to meet, let's actually take all considerations of probability theory at all out of the discussion. Here's your challenge: Show how to create a local state of three particles such that they will give quantum-mechanically acceptable results *on a single run* no matter which of the four possible relevant experimental configurations is chosen. On a single run. No statistics. No averages.No measuring more than one thing by any of the three experimenters.

You can't do it. The proof is so obvious that anyone can follow it. No averages, so no issues about averages. Put up or shut up.

By the bye, the logic of the conclusion of your paper is this: you think that because you derived an inequality by making a certain manifestly ridiculous assumption you have "proven" that other derivations make the same ridiculous assumption. There is an obvious reason no one finds it necessary to respond.

Although I cannot be certain, let me assume that the above post is indeed from the philosopher called Tim Maudlin. Here is my point-by-point response to his post:

(1) The real reason why no one has been able to meet my challenge --- including Tim Maudlin --- is because it is impossible to meet without a sleight of hand.

(2) I agree with his statement that "the issue of locality has been settled and understood for a long time..." I settled it back in 2007 in my very first paper on the subject. In this paper, I showed that --- contrary to the claims made by Bell and his followers --- quantum mechanics can indeed be completed by a locally-causal theory. In the past 10 years considerable progress has been made in this direction. Not only the GHZ state Maudlin mentions, but ALL quantum correlations can be reproduced in a locally-causal manner. I have shown this explicitly and with considerable detail, especially in this paper: http://philsci-archive.pitt.edu/13019/.

(3) Now let me come to Maudlin's counterchallenge to me, which is: "Show how to create a local state of three particles such that they will give quantum-mechanically acceptable results *on a single run* no matter which of the four possible relevant experimental configurations is chosen. On a single run. No statistics. No averages. No measuring more than one thing by any of the three experimenters."

Well, I will be happy to take up his challenge if he can tell us what the quantum mechanical prediction is for "a single run" for the GHZ state. He doesn't have to spell out the prediction here. Just give us a textbook reference, with equation numbers, providing us the quantum mechanical prediction for "a single run." Many thanks.

(4) Finally, I don't agree with his last "By the bye" comment about my paper. My paper is quite carefully written and brings out the central absurdity of Bell's argument.

Now it is impossible to derive the upper bound of 2 on the first expression involving four separate expectation values, and that is the lesson of my unmet challenge.

But the Bell-believers like Richard D. Gill claim that, since the two expressions are mathematically identical at least in the infinite limit, we can and are allowed to consider the second expression, which is trivially bounded by 2 (see, for example, https://arxiv.org/abs/1704.02876).

The problem is that the second expression is an average over physically impossible events in any possible world, classical or quantum. In other words, physically it is pure nonsense. And therefore the bound of 2 is pure nonsense. It has nothing whatsoever to do with locality or realism.

Yes, that was the real Tim Maudlin. And that did not turn out well. What surprised me is that he even bothered to engage in that discussion.

Yeah, it sure didn't turn out so well for Maudlin. He kept proposing something other than Joy's model. I'm not surprised at all since he is just another typical Bell fan troll that had no intention whatsoever of trying to understand the model. Locked up in flatland and probably stuck there forever.

***Let me note that for the 4-particle GHZS state the condition E(a, b, c, d) = << ABCD >> = +1 or -1 for some specific settings for all runs and thus even for a single run is similar to the familiar condition E(a, b) = << AB >> = +1 or -1 for the 2-particle EPRB state for some specific settings (i.e., for a = b and a = -b, respectively) for all runs and thus even for a single run. In the latter example, it is the condition of perfect correlation (or perfect anti-correlation), which is predicted by quantum mechanics.

In other words, there is absolutely nothing mysterious about ABCD = +1 and ABCD = -1 for a single run, for some specific settings, for the GHZS state. But Tim Maudlin wrongly thought that my 7-sphere model for the GHZS state predicts ABCD = +1 always, regardless of the settings a, b, c, and d. His mistake is exactly the same as the one repeatedly made by Richard D. Gill, Scott Aaronson, and James Owen Weatherall. They have all wrongly claimed that my 3-sphere model for the 2-particle EPRB state predicts E(a, b) = << AB >> = -1 always, for all settings a and b. The actual prediction of my 3-sphere model is E(a, b) = - a . b, and analogously for E(a, b, c, d):

Both mistakes --- the one made by Tim Maudlin in the GHZS case and the one made by Richard D. Gill, Scott Aaronson, and James Owen Weatherall in the EPRB case, stem from ignoring the conservation law for the spins --- namely, the physical fact that the total zero initial spin is conserved throughout each run of the experiment.

So here is a real puzzle: Not only do we learn about the conservation of angular momentum in Physics-101, it has been explicitly discussed in several of my papers on the subject. See for example equations (65) and (66) of this paper for the EPRB case and equations (143) and (144) of this paper for the GHZS case. What is more, the four individuals -- Tim Maudlin, Richard D. Gill, Scott Aaronson, and James Owen Weatherall -- are not exactly dummies. They all have professorial positions in highly respectable universities. Moreover, they are all members of the Foundational Questions Institute (FQXi). Although I myself have resigned from the institute because of their hypocrisy and politics, it is undoubtedly a prestigious institute, at least because of the sheer number of high-profile scholars they have managed to accumulate.

And yet these individuals have repeatedly made the mistake of ignoring the conservation of angular momentum in considering either EPRB or GHZS type experiments.

Here is the answer to this puzzle:

None of the four individuals is a physicist. One of them is a third-rate statistician, another is a computer plumber, and the remaining two are mediocre philosophers.